Characterizing the variability across timescales is important for understanding the underlying dynamics of the Earth system. It remains challenging to do so from palaeoclimate archives since they are more often than not irregular, and traditional methods for producing timescale-dependent estimates of variability, such as the classical periodogram and the multitaper spectrum, generally require regular time sampling. We have compared those traditional methods using interpolation with interpolation-free methods, namely the Lomb–Scargle periodogram and the first-order Haar structure function. The ability of those methods to produce timescale-dependent estimates of variability when applied to irregular data was evaluated in a comparative framework, using surrogate palaeo-proxy data generated with realistic sampling. The metric we chose to compare them is the scaling exponent, i.e. the linear slope in log-transformed coordinates, since it summarizes the behaviour of the variability across timescales. We found that, for scaling estimates in irregular time series, the interpolation-free methods are to be preferred over the methods requiring interpolation as they allow for the utilization of the information from shorter timescales which are particularly affected by the irregularity. In addition, our results suggest that the Haar structure function is the safer choice of interpolation-free method since the Lomb–Scargle periodogram is unreliable when the underlying process generating the time series is not stationary. Given that we cannot know a priori what kind of scaling behaviour is contained in a palaeoclimate time series, and that it is also possible that this changes as a function of timescale, it is a desirable characteristic for the method to handle both stationary and non-stationary cases alike.

中文翻译：

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比较古气候时间序列中时间标度的估计技术

表征跨时间尺度的可变性对于理解地球系统的基本动态非常重要。从古气候档案中做到这一点仍然具有挑战性，因为它们通常是不规则的，而产生依赖于时间尺度的可变性估计的传统方法，如经典周期图和多锥谱，通常需要定期采样。我们比较了那些使用插值的传统方法和无插值的方法，即 Lomb-Scargle 周期图和一阶 Haar 结构函数。这些方法在应用于不规则数据时产生与时间尺度相关的可变性估计的能力在比较框架中进行了评估，使用由实际采样生成的替代古代理数据。我们选择比较它们的度量是缩放指数，即对数转换坐标中的线性斜率，因为它总结了跨时间尺度的可变性行为。我们发现，对于不规则时间序列中的缩放估计，无插值方法优于需要插值的方法，因为它们允许利用来自更短时间尺度的信息，这些信息特别受不规则性的影响。此外，我们的结果表明 Haar 结构函数是无插值方法的更安全选择，因为当生成时间序列的基础过程不平稳时，Lomb-Scargle 周期图是不可靠的。鉴于我们无法先验地知道古气候时间序列中包含什么样的标度行为，